能被210整除,恰好有90个质因数的自然数有多少个
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解决时间 2021-04-04 06:58
- 提问者网友：轮囘Li巡影
- 2021-04-04 04:06
能被210整除,恰好有90个质因数的自然数有多少个
最佳答案
- 五星知识达人网友：低音帝王
- 2021-04-04 05:11
能210=2*3*5*7整除则必2357幂些幂（都于0）妨别设a,b,c,d
90数则
(a+1)(b+1)(c+1)(d+1)=90=2?3?3?5
妨取
a+1=2
b+1=3
c+1=3
d+1=5
即
a=1,
b=2
c=2
d=4
即
2*3^2*5^2*7^4=1080450
全部（共90） 整除：1,2,3,5,6,7,9,10,14,15,18,21,25,30,35,42,45,49,50,63,70,75,90,98,105,126,147,150,175,210,225,245,294,315,343,350,441,450,490,525,630,686,735,882,1029,1050,1225,1470,1575,1715,2058,2205,2401,2450,3087,3150,3430,3675,4410,4802,5145,6174,7203,7350,8575,10290,11025,12005,14406,15435,17150,21609,22050,24010,25725,30870,36015,43218,51450,60025,72030,77175,108045,120050,154350,180075,216090,360150,540225,1080450追问问的是有90个质因数的自然数有几个？
90数则
(a+1)(b+1)(c+1)(d+1)=90=2?3?3?5
妨取
a+1=2
b+1=3
c+1=3
d+1=5
即
a=1,
b=2
c=2
d=4
即
2*3^2*5^2*7^4=1080450
全部（共90） 整除：1,2,3,5,6,7,9,10,14,15,18,21,25,30,35,42,45,49,50,63,70,75,90,98,105,126,147,150,175,210,225,245,294,315,343,350,441,450,490,525,630,686,735,882,1029,1050,1225,1470,1575,1715,2058,2205,2401,2450,3087,3150,3430,3675,4410,4802,5145,6174,7203,7350,8575,10290,11025,12005,14406,15435,17150,21609,22050,24010,25725,30870,36015,43218,51450,60025,72030,77175,108045,120050,154350,180075,216090,360150,540225,1080450追问问的是有90个质因数的自然数有几个？
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